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Downlink SCMA Codebook Design with Low Error Rate by Maximizing Minimum Euclidean Distance of Superimposed Codewords
Sparse code multiple access (SCMA), as a codebook-based non-orthogonal
multiple access (NOMA) technique, has received research attention in recent
years. The codebook design problem for SCMA has also been studied to some
extent since codebook choices are highly related to the system's error rate
performance. In this paper, we approach the SCMA codebook design problem by
formulating an optimization problem to maximize the minimum Euclidean distance
(MED) of superimposed codewords under power constraints. While SCMA codebooks
with a larger MED are expected to obtain a better BER performance, no optimal
SCMA codebook in terms of MED maximization, to the authors' best knowledge, has
been reported in the SCMA literature yet. In this paper, a new iterative
algorithm based on alternating maximization with exact penalty is proposed for
the MED maximization problem. The proposed algorithm, when supplied with
appropriate initial points and parameters, achieves a set of codebooks of all
users whose MED is larger than any previously reported results. A Lagrange dual
problem is derived which provides an upper bound of MED of any set of
codebooks. Even though there is still a nonzero gap between the achieved MED
and the upper bound given by the dual problem, simulation results demonstrate
clear advantages in error rate performances of the proposed set of codebooks
over all existing ones not only in AWGN channels but also in some downlink
scenarios that fit in 5G/NR applications, making it a good codebook candidate
thereof. The proposed set of SCMA codebooks, however, are not shown to
outperform existing ones in uplink channels or in the case where
non-consecutive OFDMA subcarriers are used. The correctness and accuracy of
error curves in the simulation results are further confirmed by the
coincidences with the theoretical upper bounds of error rates derived for any
given set of codebooks.Comment: 15 pages, 12 figures. This work has been submitted to the IEEE for
possible publication. Copyright may be transferred without notice, after
which this version may no longer be accessibl